About: Hyperfactorial array notation   Sponge Permalink

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Now we need to define arrays. Each array consists of a finite sequence of zero or more entries. Each entry consists of either a positive integer or another array (and these arrays can only nest finitely). An example of a valid array is [1,1,[1,2,[3],4,[],1,1],1,3,10,1,[4,[4,3,1],5,6],1,[1,2],1,1] First, we define the following notation: \(n!m = n\uparrow^{m}(n-1)\uparrow^{m}(n-2)\cdots 4\uparrow^{m} 3 \uparrow^{m} 2 \uparrow^{m} 1\)

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  • Hyperfactorial array notation
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  • Now we need to define arrays. Each array consists of a finite sequence of zero or more entries. Each entry consists of either a positive integer or another array (and these arrays can only nest finitely). An example of a valid array is [1,1,[1,2,[3],4,[],1,1],1,3,10,1,[4,[4,3,1],5,6],1,[1,2],1,1] First, we define the following notation: \(n!m = n\uparrow^{m}(n-1)\uparrow^{m}(n-2)\cdots 4\uparrow^{m} 3 \uparrow^{m} 2 \uparrow^{m} 1\)
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  • Now we need to define arrays. Each array consists of a finite sequence of zero or more entries. Each entry consists of either a positive integer or another array (and these arrays can only nest finitely). An example of a valid array is [1,1,[1,2,[3],4,[],1,1],1,3,10,1,[4,[4,3,1],5,6],1,[1,2],1,1] First, we define the following notation: \(n!m = n\uparrow^{m}(n-1)\uparrow^{m}(n-2)\cdots 4\uparrow^{m} 3 \uparrow^{m} 2 \uparrow^{m} 1\) Hyperfactorial array notation defines a function \(n!A\), where \(A\) is an array. An example of a well-formed expression in hyperfactorial array notation is \(5![6, [7, 8], 9]\).
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